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NASA Contractor Report 182246 1
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Liquid Droplet Generation (NASA-CR-182246) L I Q U I D DhOPLET GLN E H A X ’ I 3 N ~ a 9 - 2 6 1 ~ 2
California) 72 p C S C L 20LJ F i n a l Report ( U n i v e r s i t y of Southern
Unclas G3/34 Of19621
E. P. Muntz, M. Orme, T. Farnham, G. Pham Van Diep, P. Huerre University of Southern California
Los Angeles, California
June 1989
Prepared for
Lewis Research Center
Under Grant NAS3-25068
https://ntrs.nasa.gov/search.jsp?R=19890016811 2020-04-08T23:55:14+00:00Z
Contents.
1 SUMMARY
2 INTRODUCTION
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3 JET INSTABILITY AND MULTI-STREAM DROPLET SHEETS 3
3.1 Intra-Stream Agglomeration . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.2 Multi-Stream Droplet Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 DESIGN AND FLUID SELECTION 7
4.1 General Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.2 Generator Design Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.3 Fluid Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
5 GENERATOR FABRICATION 11
0 TESTING 12
6.1 Experimental Apparatus: Droplet Dynamics Space Simulator . . . . . . . . . 13
6.2 Overall Generator Performance . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.3 Angular Dispersions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.4 Velocity Dispersions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
6.5 Power Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6.6 Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
7 ACOUSTIC ANALYSIS 18
7.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
7.1.1 Preliminary Assumptions: Effects of Viscosity . . . . . . . . . . . . . 19
7.1.2 Mathematical Model: . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
7.1.3 Normal Modes of Rectangular Cavity . . . . . . . . . . . . . . . . . . 21
7.1.4 Green’s Function of Rectangular Cavity: . . . . . . . . . . . . . . . . 22
7.1.5 Forced Response Due to Piston Motion: . . . . . . . . . . . . . . . . 23
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7.2 Results Based on Acoustic Analysis and Some Experiments . . . . . . . . . . 24
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8 LARGE SCALE GENERATOR DESIGN 25
9 SUMMARY OF RESULTS 27
APPENDIX I: NOMENCLATURE 28
REFERENCES 31
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List of Figures I ,
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Droplet profile trace obtained by positioning the optical slit on the center of
the droplet stream. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Droplet profile trace obtained by positioning the detector on the edge of the
droplet stream in order to determine the angular dispersion of the stream. ,
Response of the stream to an amplitude modulated disturbance. N is the
frequency ratio. N=l corresponds to a conventional constant amplitude sinu-
soidal waveform. . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . Distance a droplet stream can travel without significant merging with velocity
dispersion and nondimensional wavenumber as parameters. . . . . . . . . . . Schematic of assembly of several generator modules. . . . . . . . . . . . . . . Behavior of a single stream when disturbed with the cavity disturbance mode
of perturbation. Droplet fluid is DC-200: 1 x lo-' m2/s (10 cSt), nozzle
diameter is 125 microns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Behavior of a single stream when disturbed with the orifice disturbance mode
of perturbation. Droplet fluid is DC-200: lxlO-' m2/s (10 cSt) , nozzle
diameter is 125 microns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic of cross-section of generator module illustrating means of pertur-
bation chosen for present design. . . . . . . . . . . . . . . . . . . . . . . . . . Schematic of the details of orifice array assembly. . . . . . . . . . . . . . . . Schematic of the apparatus used to test the multi-stream droplet generator:
Droplet Dynamics Space Simulator. . . . . . . . . . . . . . . . . . . . . . . . Detector used to observe the droplet streams. . . . . . . . . . . . . . . . . . Schematic of optical path and data retrieval methods. . . . . . . . . . . . . . Photograph illustrating the generator performance with the 100 hole array
which was manufactured by Du Pont Precision. . . . . . . . . . . . . . . . . Droplet stream waveform (lower trace) and perturbation waveform (upper
trace) obtained from the 100 hole Du Pont Array. . . . . . . . . . . . . . . .
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... 1 l l
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Schematic of four hole NASA Lewis array. . . . . . . . . . . . . . . . . . . . Velocity dispersions as a function of non-dimensional wavenumber for streams
generated from orifice #1 of the NASA Lewis array with l ~ l O - ~ m2/s (10 cSt)
DC-200 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Velocity dispersions as a function of non-dimensional wavenumber for streams
generated from orifice #2 of the NASA Lewis array with I X ~ O - ~ m2/s (10 cSt)
DC-200. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Velocity dispersions as a function of non-dimensional wavenumber for streams
generated from orifice #3 of the NASA Lewis array with lxlO-' m2/s (10 cSt)
DC-200. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Velocity dispersions as a function of non-dimensional wavenumber for streams
generated from orifice #l of the NASA Lewis array with 4 ~ 1 0 - ~ m2/s (40 cSt)
DC-200 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Velocity dispersions as a function of non-dimensional wavenumber for streams
generated from orifice #2 of the NASA Lewis array with 4x1W5 m2/s (40 cSt)
DC-200 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Velocity dispersions as a function of non-dimensional wavenumber for streams
generated from orifice #3 of the NASA Lewis array with 4x10-' m2/s (40 cSt)
DC-200. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General configuration for acoustic analysis. . . . . . . . . . . . . . . . . . . . Results of acoustic analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . Results of acoustic analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . Prediction of cavity pressure as a function of frequency for the cavity distur-
bance mode of operation. Experimental points are absolute values since no
documentation of phase was made. . . . . . . . . . . . . . . . . . . . . . . . Prediction of cavity pressure as a function of frequency for the multi-stream
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generator with a single large cavity. . . . . . . . . . . . . . . . . . . . . . . .
configuration of five separate cavities; one for each array.
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27 Prediction of cavity pressure as a function of frequency for the generator
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28 Prediction of cavity pressure as a function of frequency for the generator
configuration of 20 separate cavities, four cavities to one array. . . . . . . . . Schematic of nominal 5000-orifice droplet generator. . . . . . . . . . . . . . . Schematic of .generator illustrating configuration. . . . . . . . . . . . . . . . Schematic of top view and bottom view of array holder. . . . . . . . . . . . . End cross-section view of assembled generator. . . . . . . . . . . . . . . . . . Schematic of orifice array assembly. . . . . . . . . . . . . . . . . . . . . . . .
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1 SUMMARY
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A multi-stream laboratory generator was designed and fabricated in a pre-prototype
configuration which would be potentially suitable for use with a Liquid Droplet Radiator.
The generator was tested using two orifice arrays; one drilled by NASA Lewis, and the
other fabricated by Du Pont Precision. Two fluids with viscosities of 1 ~ 1 0 - ~ m'/s (10
cSt) and 4x10-' m2/s (40 cSt) were also used. Stream speeds were 10, 20, and 30 m/s.
Angular dispersions of the streams from the 100 orifice Du Pont array were measured and no
significant variation with stream velocity was found. The 4x10-' m2/s (40 cSt) fluid appears,
at around fgprad, to have smaller angular dispersion than the I X ~ O - ~ m2/s (10 cSt) fluid.
However, the resolution obtained when photographing the 4x10-' m2/s (40 cSt) streams
was much greater than the resolution obtained when photographing the 1 ~ 1 0 ' ~ m2/s (10
cSt) streams and in retrospect there was a possibility of dissolved gases in the fluid during
the 10 cSt experiments. Velocity dispersions were also measured. It was discovered that in
the parameter range that was investigated, the amplitude of the disturbance applied to the
stagnation cavity is an important parameter in obtaining ultra-coherent streams of droplets.
It is also presumed that the more viscous fluid requires a higher power to the crystal (larger
crystal deflection) than does the lower viscosity fluid, although this presumption must be
verified in future investigations. The velocity dispersions for streams from several positions
along the 0.13 m orifice array were similar.
A conceptual design for a 5200 stream generator was completed, incorporating ways
to generate higher disturbance amplitudes than was possible in the laboratory generator.
Otherwise the design is similar to that of the laboratory generator.
2 INTRODUCTION
An important application for droplet streams in space is the proposed liquid droplet
radiator (LDR),l which would operate by employing a large number of free-flying droplet
streams as the radiating element of a heat rejection system for high power space stations.
A number of techniques for generating droplet streams have been considered2. The method
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of drop generation which is implemented here is the breakup of a 100 pm diameter capillary
jet into uniformly separated drops by applying a periodic surface displacement. This study
is focused on the design of a multi-stream generator which is a module in a pre-prototype
flight configuration for. use with the LDR. It was designed such that an arbitrary number of
modules can be joined together to produce the required number of droplet streams for the
LDR. For example, in order to radiate 10' W of thermal energy, about 10' droplet streams
are required.
To maintain efficiency in the proposed applications, it is desirable that droplet collisions
are minimal, which is realized if the streams of free-flying liquid drops remain parallel, and
the droplets within each stream remain unagglomerated for the duration of their flight.
Both issues of stream parallelism and droplet separation are addressed in the design. The
prevention of intra-stream droplet agglomeration depends on maintaining the uniformity of
the intra-stream droplet separation over the fight distance and is largely dependent on the
form of the disturbance applied to the stream. A new method of droplet generation, which
increases the uniformity of the droplets by up to an order of magnitude compared to the
conventional modes of droplet generation, is implemented in the design. Both the new and
conventional modes of droplet stream production will be described in Section 3.
Stream parallelism is largely a matter of precision manufacturing and hardware design.
The intrinsic directional stability of a single stream is high, having been measured to be
typically around f2prad. This is illustrated by the results shown in Figures 1 and 2. The
results were obtained by positioning the magnified image of the droplet stream onto a slit
which was parallel to the stream's axis and just in front of a photomultiplier tube. The
slit height was arranged to be approximately equal to the diameter of a magnified droplet
image while its width was much less. In Figure 1, the droplet images were centered on the
slit. In Figure 2, the edges of the droplet images were positioned close to the slit. The
fluctuating amplitudes of the droplet signals as seen in Figure 2 compared to Figure 1 give
a very sensitive indication of the position of each droplet lo,ll and give, in this case, an
angular dispersion of f lprad. The stream parallelism is thus primarily dependent on the
parallelism of the nozzle arrays from which the streams are generated, on nozzle exit surface
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wetting, on deflections of the orifice plate, and on nozzle clogging.
The report it3 organized in seven major parts which follow the framework of the con-
tract. Section 3 gives some background concerning the fluid mechanics, jet instability and
multi-stream droplet sheets. Section 4 deals with the design of the generator, including
considerations such as: methods of applying radial stream disturbances, eliminating angular
deflection of the array when subjected to the maximum load required, eliminating angular
twist of the array which may result if the surface of the array is not seated properly in the
generator, and the working fluid selection. Section 5 is concerned with the.fabrication of the
generator. Section 6 describes the performance, testing and results for the generator oper-
ating at specified conditions. Section 7 describes the results of an acoustic analysis which
deals with the generation of stagnation chamber pressure disturbances from nozzle motion,
and Section 8 deals with the large scale generator design and describes the accompanying
conceptual design drawings. Finally, a summary of the work done, results obtained, and
areas in need of further investigation follow in Section 9.
3 JET INSTABILITY AND MULTI-STREAM DROPLET SHEETS
In this section the consequences of the droplet speed dispersion observed in the generation
of droplets from capillary streams are reviewed. Droplet speed dispersion affects intra-stream
agglomeration of droplets. Also, the requirements placed on a generator by attempting to
minimize inter-stream collisions due to lack of parallelism are described.
3.1 Intra-Stream Agglomeration
Typically, a controlled instability of a fluid stream is introduced by disturbing the stream’s 3 4 surface with a sinusoidal waveform. Plateau and Savart were the first to observe that when
a fluid stream is periodically disturbed, the stream breaks into a series of equally spaced
droplets which are separated a distance corresponding to the wavelength of the disturbance.
Lord Rayleigh5 developed the linear stability analysis of the unstable jet and found that
the disturbance on the stream will be unstable, and break into drops if the wavenumber of
the disturbance is greater than the stream circumference. He showed that the surface waves
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grow exponentially in time as @‘, where p is the amplification factor. He showed further
the maximum amplification factor occurred at a nondimensional wavenumber (which is the
wavenumber of the disturbance multiplied by the radius of the jet) of 0.697 for an inviscid
fluid. Subsequent to the analysis of Rayleigh, there has been a rich development of linear
and nonlinear theories which describe the instabilities of the surface waves along with careful
experiments investigating jet i n ~ t a b i l i t i e s ~ , ~ , ~ . Most of the theories, with the exception of
Chaudhary and Redekopp’ , address the same problem: the response of a stream to imposed
sinusoidal oscillations. Most of the experiments have addressed the problem of the breakup
distance and the corresponding breakup time of a fluid stream when the stream is perturbed
with a sinusoidal disturbance and injected into atmospheric conditions.
Chaudhary and Redekopp imposed on the stream a sinusoidal disturbance with an added
harmonic, in order to suppress satellite occurrences. Satellite drops are smaller drops which
may appear in-between the main drops and result from nonlinearities in the breakup process.
For the application of ink jet printing, the occurrence of s a t a t e drops is very undesirable.
Two of the present authors have recently discovered lo a new disturbance waveform
that dramatically improves the control of the droplet stream configuration and subsequent
propagation. The technique has been shown to greatly reduce the intra-stream agglomeration
over the conventional methods of perturbation, Le., a sinusoidal disturbance, or a sinusoidal
disturbance with an added harmonic. The new method of perturbation is considered a
desirable feature of an LDR generator design by the present authors. The droplet production
technique involves the use of an amplitude modulated sinusoidal waveform, and is discussed
in detail in Ref 11. In brief, the fluid responds to the amplitude modulated disturbance by
first breaking into droplets which are separated a distance corresponding to the wavelength
of the fast Gequency of the amplitude modulated disturbance. We call these droplets “carrier
droplets.” Unlike droplets generated with a conventional disturbance, each carrier droplet
has associated with it a predictable relative speed. The relative speed is a direct consequence
of the imposed amplitude modulated disturbance. Thus the disturbance essentially forces
the carrier droplets in two adjacent half periods of the modulation to coalesce into a single
drop. These “modulation” drops are measured to be much more stable than drops generated
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with a pure sinusoidal disturbance. A physical explanation follows.
We consider all fluctuations of mass and momentum to arise at the break points of the
fluid stream. If the break point is displaced, then one drop has an excess of momentum, and
the neighboring drop has a deficit of the same amount of momentum. When the two drops
coalesce, the fluctuations cancel, leaving the only sources of random fluctuations at the end
points of the last two drops to merge. Thus the velocity dispersion, which is a measure of
stream uniformity and is simply the ratio of the standard deviation of the unpredictable
velocity fluctuations of the drops to the average drop speed, should decrease as 1/N, where
N is the frequency ratio of the disturbance, or the number of carrier droplets that make up
one modulation drop.
Figure 3 illustrates the results of applying an amplitude modulated disturbance to a
single stream. The velocity dispersion at N=l corresponds to the dispersion generated with
a conventional waveform. The solid line represents 1/N.
Since the efficiency of the LDR depends on the high surface area to volume ratio of the
drops, it is clear that the efficiency is maintained by suppressing unplanned droplet merging
(see section 3.2). Thus, the new mode of perturbation is employed in the generator design.
The effect of droplet speed dispersions on agglomeration is illustrated in Figure 4, (from Ref.
12) where it can be seen that for a typical flight distance of a LDR (50 m) a droplet speed
dispersion of around lo-* as required to prevent significant (10% of droplets) intra-stream
agglomeration.
3.2 Multi-Stream Droplet Sheets
Consider the following example of a droplet radiator that is N, droplet (or orifice) rows
thick. The thickness of the sheet in numbers of radiation mean-free-paths is defined as
where Ad is the nominal center to center spacing of droplets in a stream which in this case is
also assumed to be the stream spacing in a row and d is the droplet diameter. The sheet’s
thickness in radiation mean-free-paths is useful to help characterize the efficiency of a droplet
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sheet as a radiator; for A < 1 the sheet emissivity varies approximately linearly with N,
or A. A simple calculation is informative. Say the A as defined above is set at 1. Assume
streams of 100 pm droplets with a center to center separation of 3.5 diameters and thus
N, “v 16. Now, assume these agglomerate due to drop to drop speed differences within each
stream. If on the average each drop combines with one other, the center to center distance
has doubled and the drop diameter has increased by 21/3, lowering A from 1 to 0.8 (note,
since inter-stream spacing would not change, A changes only due to intra-stream droplet
spacing and droplet diameters). Reducing A from 1 to 0.8 reduces the sheet emissivity by
about 20%. If there is one further merging, A=0.65 which reduces the emissivity by 35%.
Thus, modest amounts of agglomeration over a significant proportion of a sheet’s area could
have significant effects on the radiated power.
Similar comments about agglomeration also apply to inter-stream collisions caused by
the angular dispersion of the nozzles, since for relative collision velocities less than about 2
m/s, 100 pm droplets tend to coalesce when they collide, at least for near head-on collisions.
If we define three separate inter-droplet distances, Ad the intra-stream separation, Afi l the
geometric separation of the nozzles in one row and A,,, the separation between nozzle rows.
The droplet number density is given by
Assume a characteristic mean angular error of 8, in the nozzle alignment. An approximate
average relative speed of colliding droplets is v d sin e,, where vd is the speed of the droplets.
The total collision cross-section is ut = .1r8 where d is the droplet diameter. There is some
divergence due to the initial angular dispersion of the streams. Assume a droplet sheet
initially w, cm thick at the generator, thus there are w,/Afi2 = N, rows of nozzles. At some
point z from the generator the number of collisions one droplet experiences in a length dz is
Integrating, the total number of collisions for one droplet for a flight length L is
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(4) ?r@N, 2Lsin8,
N , = - m( N, Ag2 + 1) 2AdAg1
For d,=2 mad, L=50 m, N,=lO, d=100 pm, and Ad = Agl = Ag2=3.5d, the total number
of collisions per droplet as the stream travels from the generator for 50 m is N , = 5.3. If
the between-row spacing Ag2 is increased to 0.005 m (50d) Net =2, which relieves the inter-
stream collision problem considerably, although not completely by any means. Note that
if is increased to 10d, which may be necessary to prevent the streams influencing each
other due to wetting of the nozzle exit surface, the total number of collisions per droplet
becomes N,=0.7.
There are all sorts of arguments about how much droplet agglomeration is acceptable.
For the present design it was decided that the generator should provide a sheet with a small
amount (N, < 1) of agglomeration. A relaxation of this requirement might be possible d t e r
careful system optimization studies.
4 DESIGN AND FLUID SELECTION
e 4.1 General Design Considerations
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In order to identify fundamental problems associated with a flight capable design, the
multi-stream generator is designed in a pre-prototype flight configuration. With obvious
mass saving steps it could be suitable for use with a liquid droplet radiator. In this ap-
proach, any problems encountered with the operation of the generator provide practical
design considerations for an actual flight module.
The most basic decision about the generator configuration has to do with the method
that is selected to apply stream disturbances. Two possibilities have been examined. The
first is the use of a fluctuating cavity pressure in the stagnation chamber for the streams
(“cavity disturbance” mode). The fluctuating disturbance pressure that is superimposed on
the stagnation pressure causes a periodic variation in mass flow in the streams which leads to
a disturbance of the stream radii. The second possibility is to apply a disturbance directly
to the nozzle array. The moving array may directly disturb the stream through viscous
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effects at the nozzle walls. Also, the moving array can generate a fluctuating pressure in the
stagnation cavity with the disturbance then being similar to the cavity disturbance mode.
For reference purposes the moving nozzle case is distinguished by naming it the “orifice
disturbance” mode.
Fluid lost due to partially blocked nozzles generating misdirected streams is a highly
probable failure mode since small but continuous losses of fluid are fatal to the success
of the LDR. The present generator design was accomplished keeping in mind conceptual
design solutions for overcoming this problem. A pipe crawler for unplugging and/or plugging
individual nozzles and a segment isolation scheme for cutting fluid flow to a limited number of
nozzles using valves in the form of air bags or foam were hypothesized but not implemented.
The generator design is compatible with the air bag or foam solutions since these were
considered to be the simplest option. Additional particulate control to minimize nozzle
plugging is incorporated with large areas of micron level filtering.
The parallelism of the nozzle array itself must be considered in the design to obtain.the
optimum stream spacing in order to prevent fluid loss or agglomeration. At present, the best
orifice arrays that are easily obtainable can produce droplet streams with an angular standard
deviation of several milliradians. It has been suggested (Ref. 13) that the parallelism of the
nozzles in arrays may be improved with future studies.
All of the previous considerations must be integrated with the requirements of supplying
a sufficient quantity of fluid with a minimum pressure drop over distances of typically 50
meters in a minimum mass device. In the design the assumption was made that fluid would
be supplied at approximately working pressure; another option would be a high pressure
supply system with local delivery by pressure regulators to the radiator modules. In the
latter case our design would change somewhat, but not in any important way as far as the
details of the stream generation are concerned.
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4.2 Generator Design Details
The generator has been designed such that many modules may be connected in order
to produce the desired number of streams for the Liquid Droplet Radiator. A conceptual
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schematic of several connected generator modules is illustrated in Figure 5. To summarize
the design configuration, micron filtered fluid reaches each orifice array through the fluid sup-
ply duct. The height of the duct is chosen so that the pressure drop over several connected
modules is minimal (other considerations such as total fluid mass are important considera-
tions which enter into the choice of the supply duct size but must be made by optimizing the
entire LDR system). A filter plate with a pore size of 2-3 pm separates the fluid stagnation
chamber from the fluid supply duct. In the event of misdirected streams, the actual flight
model can employ the segment isolation scheme by inflating an air bag or injecting foam into
the stagnation chamber of a module. The generator design is capable of holding five orifice
arrays which are each 0.13 m in length. Each orifice is 100 microns in diameter so that for
a 5 diameter stream spacing with end clearances a single array contains 1250 orifices. For
preliminary testing a single array 0.066 m in length was used with orifice separations of 5
and 10 nozzle diameters. For final testing, a 0.13 m array with 100 orifices was studied.
We have examined two methods of applying an amplitude modulated disturbance to initi-
ate the radial instability of the stream. The first method considered is to form a disturbance
in the stagnation cavity by inserting an isolated piezoelectric crystal under the filter plate.
In this case, it is desirable to isolate the crystal from the structure in order to inhibit any un-
wanted structural vibrations. The crystal must also be shielded from the fluid since the fluid
in the liquid droplet radiator will be sufficiently hot to exceed the Curie point of the crystal.
To attain a velocity dispersion around it has been found that pressure fluctuations (in
the form of an amplitude modulated waveform with a high frequency ratio) of several percent
of the stagnation pressure are required for 40 cSt fluid1'. To reach these levels while using
the cavity disturbance mode of operation requires using a crystal that is large compared to
the separation between the crystal and the orifice or to operate at conditions corresponding
to a cavity resonance. The second mode of stream perturbation relies on nozzle motion.
In this case, the piezoelectric crystal is mounted on the exit face of the orifice array. It
is necessary to design the oscillating orifice assembly such that excessive vibrations are not
introduced into the structure. An advantage associated with orifice disturbance mode is that
it is easier to have the fluid cavity only about 0.01 m high while still supplying sufficient
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fluid to the orifice array. Also, the crystal does not come in direct contact with hot fluids.
In this mode of operation the stream disturbance originates from the pressure field at the
surface of the vibrating orifice array and from the direct influence of mechanical motion of
the orifice.
Both methods of perturbation application have been tested and yield similar results. Fig-
ures 6 and 7 illustrate the results of the uniformity of single streams of fluid when perturbed
with the cavity disturbance mode (Figure 6) and the orifice disturbance mode (Figure 7)
for streams of 1 ~ 1 0 - ~ m2/s (10 cSt) DC-200 fluid. Figures 6 and 7 were obtained with a
conventional sinusoidal disturbance applied to the fluid stream. Since the two modes of
operation give similar results, and due to the advantages described, the orifice disturbance
mode of operation has been incorporated into the generator design. Figure 8 illustrates an
enlarged cross-section of the generator module showing the piezoelectric crystal and nozzle
arrangement chosen.
The orifices have been formed directly in the oscillating assembly shown in detail in Figure
9. For operation, the piezoelectric crystal is bonded onto the exit face of the orifice array. The
crystal and array configuration are placed onto a ceramic insulating seat. Power is provided
to the crystal through a wire which feeds through the ceramic and onto a brass washer which
lies between the ceramic insulator and the piezoelectric crystal. The assembly was designed
such that the angular deflection due to bending of the orifice array when subjected to a
load of 1 . 0 3 4 ~ 1 0 ~ Pa (150 psi) is less than 5 prad. The angular twist of the array, which
may result if the surface of the crystal and the surface of the ceramic insulating seat are not
parallel, was calculated to be significantly less than one 1 mrad. Careful attempts have been
made to make the joining parts parallel.
4.3 Fluid Selection
Performance testing of the multi-stream generator was required with the use of two
different fluids having viscosities of 1x10'' and 4x10-' m2/s (10 and 40 cSt). Original plans
called for the use of DC-200 at the 1 ~ 1 0 - ~ (10 cSt) viscosity, and DC-704 at 4x10-' (40
cSt). Both fluids are silicone based low vapor pressure diffusion pump oils. DC-200 has the
4
d
4
d
4
I
10
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a
0
0
e
0
a
a
a
convenience of being available in a variety of viscosities, and it is considerably less expensive
than DC-704. However, the use of two fluids with as wide a variety in surface tension as
possible was desirable. The surface tension of DC-704 is about twice that of DC-200, thus
the two aforementioned fluids were chosen for use with the generator.
After testing the generator with the lxlO-’ (10 cSt) DC-200, and switching to the DC-
704, several practical problems were encountered. The most significant was that the two
fluids do not mix with each other. We found the DC-704 contained a suspension of the
residual traces of DC-200 left in the system. The resulting fluid appeared to have a nonuni-
form surface tension, and furthermore, data taken with the mixture was not representative
and is not included in this report. It was necessary to clean the apparatus thoroughly of the
fluid mixture. This was done by dismantling as much of the system as possible followed by
kerosene and alcohol purges. For subsequent tests DC-200, at the &lo-’ (40 cSt) viscosity
was used in lieu of the DC-704. The surface tension is not expected to have a significant
effect since the growth factor varies as ( U / P ~ ) ’ / ~ , where u is the surface tension. The density
of all these fluids is around lo3 kg/m3 so that there is not a big difference in ( U / P ~ ) ” ~ for a
factor of two difference in u.
5 GENERATOR FABRICATION
Drawings of the generator design were submitted to NASA and approved for fabrication.
The majority of the generator was fabricated in the USC School of Engineering’s machine
shop. Two different orifice arrays were made for reasons which are discusssed in Section 6.
One was fabricated by Du Pont Precision and has 100 orifices, each 100 pm in diameter by
300 pm long. It was produced from hardenable stainless steel. The orifices were measured by
Du Pont to be accurate in diameter and roundness to f 2 pm. Perpendicularity of the orifices
to the lapped reference plane was nominally specified to better than f2 mrad during the
manufacturing process. The orifices were also nominally specified to be parallel to each other
to better than f3 mrad. The second array, which was drilled in aluminum by NASA Lewis
has 4, 100 pm diameter orifices. As shown in Figure 9, array plates are bonded directly to a
piezoelectric crystal which has the shape of a “race-track.” The array and crystal assembly
11
a
rest on top of a brass washer, and the entire assembly fits in a ceramic insulating seat.
Both the ceramic seat and the “race-track” shaped piezoelectric crystal were machined by
Duramic Products Inc. and Mindrum Precision respectively. Electrical contact is made to
the piezoelectric crystal by a wire which feeds through the ceramic seat and makes contact
with the brass washer.
6 TESTING
The contract required an investigation of the operation of the droplet generator with a
0.13 m long, 100 hole array. Test conditions included the use of two different droplet fluids
of different viscosity and three different stream speeds.
Two preliminary arrays were tested prior to the machining of the final 0.13 m array in
order to uncover any problems. Each array assembly was configured as shown in Figure
9. One array was drilled by NASA Lewis, and contains 53 holes with 10 diameter spacing
between holes. The array was machined out of aluminum. The second array was machined
out of stainless steel and was fabricated by Du Pont Precision with the same tolerances as
described above. It contains 109 holes with 5 diameter spacing between holes. Each array
is 0.05598 m (2.20 inches) long and the orifices are 100 p m in diameter. The preliminary
tests showed that the array which was fabricated by Du Pont produced droplet streams which
were significantly more parallel than the array drilled by NASA Lewis. However, the angular
dispersion was great enough with the Du Pont array to prohibit the ready identification of
particular streams after they had traveled 5.5 m. For this reason, two 0.13 m arrays were
manufactured for the final testing phase. The first was fabricated by Du Pont Precision
and contained 100 holes, each 100 pm in diameter. This array was used for testing the
overall generator performance and the angular dispersion of the array. The second array
which was drilled by NASA Lewis contained 4 holes and was used for measuring the velocity
dispersions of the individual streams as a function of disturbance wavenumber. The electric
power consumed by the array oscillating in the droplet generator was measured. The several
measurements will be discussed in more detail in Sections 6.2 through 6.4.
4
4
4
12
0.1 Experimental Apparatus: Droplet Dynamics Space Simulator
a
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The facility in which the droplet streams are generated, measured and observed is the
Droplet Dynamics Space Simulator, shown in Figure 10. The apparatus is an isolated body,
suspended from its center of gravity by four vibration isolation mounts which filter motion
above frequencies of 1 Hz. The main component is a vertically suspended optical bench on
which a 5.5m long; 0.25m diameter stainless steel flight tube, two diffusion pumps, sensors
and optics are mounted. Optical access is provided to the tube at its top and bottom ends.
Recycled, out-gassed fluid is supplied to the multi-stream droplet array mounted at the top
of the fight tube. A flexible rubber diaphragm is used to separate the high pressure gas
(which drives the flow) from the droplet fluid. This is necessary since high pressure gas
dissolves in the fluid, leading to cavitation when the fluid is ejected into a vacuum.
The piezoelectric crystal which initiates the stream instability is driven by two phase-
locked function generators that are controlled by a high-stability reference source. The func-
tion generators are used to provide a stable, amplitude-modulated signal. For a conventional
constant amplitude sinusoidal signal, only one generator is needed.
The detector used to image the droplet streams at the lower observation port is illustrated
in Figure 11. The image of the droplet stream is superimposed onto the receiving slit of the
detector. The detector essentially consists of a receiving slit which is positioned perpendicular
to the image of the droplet stream, and just in front of a photomultiplier tube. The shadow
image is then passed through a cylindrical lens in order to illuminate a large portion of
the photomultiplier tube’s photocathode. Careful attempts were made in the design of the
detector in order to capture an accurate representation of the droplet stream profile. The
design characteristics of the detector are discussed in detail in Ref. 12.
A schematic of operation is sketched in Figure 12. To measure the uniformity of the
droplet stream, a light beam is split and sent through the optical access ports. The beam
is sent through a spatial filter in order to filter out any optical noise due to particulates
entering the light field. As the droplet stream passes through the light, its magnified shadow
image is reflected onto the receiving slit of the detector. Each droplet image that passes over
the slit causes a dip in the light flux received by the slit. The corresponding signal consists
13
4
of a series of dips representing droplets. The output signal from the photomultiplier tube is
digitized and recorded with a waveform recorder at selectable rates up to 20 MHz, and the
resulting digital codes are stored in up to 16k words of memory. Once stored in memory, the
recorded droplet stream waveform is output in both digital and analog formats and stored
for later evaluations and measurements by computer. Typically, waveforms consisting of up
to 400 droplets were captured and analyzed.
6.2 Overall Generator Performance
The overall generator performance was measured withathe use of still photography. Pre-
liminary tests were made with two small orifice arrays as discussed previously. One array
had 53 holes with a 10 droplet diameter spacing, and the other had 109 holes spaced 5
droplet diameters apart. No significant differences were found in the performance of the two
arrays, or interactions between the streams due to surface wetting. Final testing was done 4
4
with two 0.13 m arrays; one with 100 holes which was fabricated by Du Pont Precision, and
one with four holes used for velocity dispersion measurements which was drilled by NASA
Lewis. Figure 13 is a photograph of the 0.13 m, 100 hole array in operation. In this par-
ticular photograph, the droplet fluid is DC-200 at 4 X l O - ' m2/s (40 cSt), and the stream's
speed was 40 m/s. Similar photographs were taken for the other conditions. The specifics
of the angular dispersion and the velocity dispersions of the streams will be discussed in the
following sections.
4
4
6.3 Angular Dispersions
The angular dispersion of the 100 hole array was measured with the following method.
First, a laser sheet was created which was several centimeters wide, several millimeters thick
and spanned the horizontal distance of the observation chamber. By allowing the droplet
streams to travel through the laser sheet in an approximately perpendicular direction, and by
photographing the resulting forward scattering, we have been able to determine the angular
spread of the array of streams. For data reduction, a photograph was taken of a grid which
was placed in the chamber at the same orientation as the laser sheet. Deviations of the
4
4
14
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stream's displacements from the centerline of the array were measured by superimposing the
images of the scattered light patterns from the streams and the grid. A standard deviation of
the angular spread was found by measuring the deviation of each stream from the centerline,
forming an average displacement and calculating the standard deviation. Table 1 gives the
results of the angular dispersion measurements at the indicated conditions. All measurements
are in mrad. The result indicated with an asterisk is an estimated standard deviation, for
in this case trouble was encountered separating the images of the scattered light due to
overexposed film. Note that the angular dispersion that was calculated is for the direction
perpendicular to the line of orifices. The higher dispersion observed for the 10 cSt fluid
has no obvious explanation. Generally it is observed that angular dispersions are sensitive
to dissolved gas in the liquid. The 10 cSt experiments were the initial experiments in this
study. It is possible that because they also involved a first use of a new high capacity oil
recirculation system, some dissolved gas may have been present in these experiments.
Table I Angular Dispersions Perpendicular to Orifice Row (mrad) for a 109 Stream Array
0
0
II I DC-200, lOcSt I DC-200,40cSt 11 10 m/s
20 m/s
30 m/s 11.5' 8.9
6.4 Velocity Dispersions
Both arrays were studied to measure velocity dispersions using both fluids. The unifor-
mity of a single stream from the 109 hole array with the IxlO-' m2/s (10 cSt) fluid was
measured and it was found that the stream had a velocity dispersion of 1.25xlO-' when
perturbed with an amplitude modulated waveform with a frequency ratio of 4:l. A trace of
this droplet waveform is illustrated in Figure 14. Following this experiment, the NASA four
hole array was tested (Figure 15). It was only possible to analyze the performance of three
of the streams, as the fourth orifice was misdirected at an extreme angle, and the apparatus
15
4
could not be maneuvered enough to locate it. Figures 16, 17, and 18 illustrate the array
performance, where orifices #1, #2, and #3 are in consecutive order as they appear on the
array. It can be seen that all orifices tested respond generally in the same way. For these re-
sults, the streams were perturbed with an amplitude modulated waveform with a frequency
ratio of 4:l. When the streams were perturbed with a conventional sinusoidal waveform
they were observed to be less uniform. Only the data points generated with an amplitude
modulated waveform with a frequency ratio of 4:l were saved and are included in Figures
16 through 18. From the figures it can be seen that the velocity dispersions are as high as
lxlO-'. The measurements are not as low as the measurement obtained with the Du Pont
array. This finding was investigated in a preliminary way and it appears that the difference
in uniformity was due to a difference in the perturbation amplitude which was applied to
the stream. When the NASA Lewis array was tested, the power amplifier was unserviceable.
Unfortunately, use had to be made of an amplifier which outputs - 10 V. The amplifier that
was used to test the Du Pont array typically outputs - 70 V. In retrospect, it appears that
the disturbance amplitude was in a region where higher voltage to the piezoelectric crystal
is necessary for obtaining ultra-coherent streams of drops (with velocity dispersions near
1 ~ 1 0 ' ~ ) from the array, when using the orifice disturbance mode of operation along with
an amplitude modulated disturbance at large frequency ratios. We are currently studying
the effects of absolute amplitude of the driving perturbations on the velocity dispersion of
the breakup of a single stream of drops. At this stage in the investigation, it appears that
the amplitude plays a significant role in the velocity dispersion of the drops for the range of
disturbance amplitude that was employed in the tests described previously.
Following the work with the lxlO-' m2/s (10 cSt) fluid, a switch was made to the 4x10-'
m2/s (40 cSt) fluid. DC-200 was used in both cases as discussed in Section 4.3. For this
work, the amplifier which output - 70 V was available for all measurements. Measurements
with both the Du Pont array and the NASA Lewis array were similar. Figures 19, 20, and
21 illustrate the NASA array performance with the 4X10-5 m2/s (40 cSt) fluid. For each
data point, the streams were perturbed with an amplitude modulated disturbance with a
frequency ratio of 4:l . For reasons that are not known it was only possible to test the
4
4
16
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array at 20 m/s and at 30 m/s when using the 4XlO-’ m2/s (40 cSt) fluid. The 10 m/s
stream’s velocity dispersion was very high, which was unexpected. It can be seen that the
velocity dispersions for the 20 and 30 m/s are for the most part near a few times lo-‘,
which by the current standards at USC (when using an amplitude modulated disturbance
at large frequency ratios) are considered to be about an order of magnitude high. One
plausible explanation for these results is that the orifice disturbance mode of operation had
not previously been tested with a highly viscous fluid. In other studies at USC, highly viscous
fluids were tested only while using the cavity disturbance mode. It is believed that the cavity
disturbance mode as it was used in that work provided a greater amplitude disturbance than
the orifice disturbance mode. A greater disturbance amplitude may be necessary to breakup
the more viscous fluids into droplet streams with very low velocity dispersion (see following
section on acoustic analysis and resulting design implications).
0.5 Power Measurement
0
0
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Power measurements were made for typical generator operating conditions of 100 psi,
and 50kHz carrier frequency, 40 cSt fluid and the 0.13 m long orifice array. The measure-
ments were obtained by observing voltage drops using a differential plug-in amplifier for an
oscilloscope and a 6Sl resistor in the supply line to the piezoelectric crystal. The resistor
was about 0.5 m from the crystal. The supply line was loaded with a lO‘Sl shunt to ground
between the 6R resistor and the power supply. Simultaneous measurements using a dual
beam oscilloscope were made of the applied voltage and the current passing through the 6
Sl resistor. It was observed at 50 kHz that the voltage and current were in- phase and corre-
sponded to an average power consumption of 6.5 watts. This compares to an average current
flow of about 0.05 amps required to charge the capacitor (the RC time constant of the 652
piezoelectric circuit is less that lO-’s). The power required to move a piston against 100
psi from the minimum to maximum deflection of the crystal (about 0.2 pm) 50 x lo3 times
a second is around 8 watts, assuming that the energy injected into the fluid is completely
dissipated.
17
6.6 Satellites
For streams disturbed with an amplitude modulated disturbance the existence of satellites
is not expected after the streams have coalesced to modulation drops. For the measurements
done in this study no satellites were observed.
Parameter
L,
Lv
L z
7 ACOUSTIC ANALYSIS
Typical Value
0.10 m
0.10 m
0.02 m
In order to help understand the mechanisms by which a disturbance is applied to the
droplet stream from the generator, both theoretical and experimental studies have been
completed. The theoretical work is detailed in Section 7.1 and the experiments in Section
7.2.
100 kg/m3 I l l
Table 2
Parameter Values Used in the Acoustic Analysis
I II
0.01 m
0.01 m
0.1 x W 6 m
U 14.16 x lo-' m2/s
7.1 Theory
Consider a rectangular cavity with characteristic dimension L,, L,, L, subjected to
external forcing by means of a rectangular piston with side lengths C,, e,. The geometrical
18
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configuration is sketched in Figure 22. The parameters E and w denote the amplitude and
circular frequency of the excitation, respectively. The medium is assumed to be homogeneous
and at rest, of density po and speed of sound c. Kinematic viscosity is Y, dilatational viscosity
is 7 . Typical values of-interest for all these parameters are listed in Table 2. The main purpose
of the present calculation is to obtain the value of the perturbation pressure at the center of
the piston as a function of forcing frequency and of the other parameters in the problem.
7.1.1 Preliminary Assumptions: Effects of Viscosity
According to classical results 14,15,16 a plane wave ei(kt-ot) moving in a duct of cross-
sectional length scale L filled with a viscous and heat-conducting fluid, is characterized by e
the following complex wavenumber k
0
e
2
+ L)E ( 5 ) ++-E- Po" c3 ' w l + i 7-1 (vw)1/2 i 7-1 c f i f i CL
k x - + -(I+ -)
where y is the ratio of specific heats and Pr the Prandtl number. In this expression, the first
term is the classical propagation term of inviscid sound waves in an unbounded medium.
The second term represents attenuation and dispersion effects due to the presence of viscous
Stokes layers (unsteady perturbation boundary layers) at the walls of the tube. The thickness
of these layers is of order 6 - [ ( ~ v ) / w ] ' / ~ . Finally, the third terms accounts for dilatational
attenuation~of acoustic waves in the bulk of the fluid. We shall assume that the excitation
frequency is such that the hierarchy of these various terms is respected, namely
0
e
VW2 (vw)1/2 < CL (6% b)
(vw) ' / f 0 < - and - C L C c3
Under these conditions, dissipation effects can be neglected altogether. Thus the range
of frequencies of interest is restricted to be
V (7)
The first inequality states that viscous dissipation in the Stokes layers is negligible whereas
the second inequality states that bulk dissipation is negligible compared to Stokes layer
19
dissipation. For the values listed in Table I, it is therefore legitimate to neglect at leading
order viscous damping, provided the excitation frequencies are chosen within the range
4 . 1 0 - ~ a a io6
These conditions appear to be satisfied in practice and we shall neglect viscous dissipation
effects.
7.1.2 Mathematical Model:
The governing equations of linear sound propagation in a fluid medium at rest are given
by
g + pov . Q = 0
f3v P o x = -VP (9)
p = c2p ( 1 0 )
where p, p and
boundary conditions are
denote the perturbation density, pressure and velocity, respectively. The
Q ii = o on all walls except piston, (W
In the above, the piston displacement Zp =
of the perturbation velocity is denoted by w .
and Zis the unit normal. The 2-component
It is convenient to reformulate the entire problem in terms of perturbation pressure only.
One readily obtains the following system:
I
4
20
4
V, . n' = 0 on all walls except piston
2 = po~w2e-'"*(13b) a z
on a
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7.1.3 Normal Modes of Rectangular Cavity
The natural modes of the cavity can be sought in the absence of external excitations. We
look for solutions of the form
p = $ ( ~ , y , z ) e - ' ~ ~
After substitution into the previous system, one obtains the eigenvalue problem
where k = w / c is the unknown eigenvalue
Resonances can be determined by a straightforward separation-of-variable analysis. The
eigenfunctions are found to be
and the corresponding eigenvalues, or resonance frequencies, are given by
e
0 The indices n, ,ny,n, may take all zero or positive integer values. The eigenfunctions are
endowed with the following orthogonality properties:
21
For simplicity we have denoted by n or m distinct triads (n,, ny, n,). The symbol 6,, is the
Kronecker delta
1 m = n
0 m # n amn =
and the quantity An is such that
1 1 n,=O
EnzEnyEns 2 n,>O An =
The quantity V is the cavity volume V = L,L,,Lz.
a
7.1.4 Green’s Function of Rectangular Cavity:
For future use, it is necessary to obtain the impulse response (or Green’s function) of
the cavity when it is subjected to a delta-function excitation of frequency w at an arbitrary
location Fo. The mathematical problem of interest is then
V2Gw + k2Gw = 6(F- Fo) (21)
VG - n’ = 0 on all walls
Upon assuming an expansion of G, in the previous eigenfunctions, one generates the solution
As before, triads (n,, ny, n,) are given the collective name n. Note that the above impulse
response blows up at the resonant frequencies wn = ckn, as expected.
1
1
22
1
7.1.5 Forced Response D u e to Piston Motion:
One may now tackle the original problem at hand specified by equations (12)-(13).
Steady-state solutions are sought in the form
P ( Z , Y , Z , t ) = Pw(z ,Y ,Z)e- iwt
where w is the excitation frequency specified in (9b). The unknown p , satisfies
V 2 p w + k2p, = 0
(23)
(24) a
V p w n' = 0 on all walls except piston surface (254
0
0
(h
0
(25b) + v p , - n = poew2 on piston surface s at z = - ~ , / 2 a p w
an - =
A straightforward application of Green's theorem allows us to relate the values of the pressure
gradient at the piston surface to the pressure field p , within the cavity. One obtains the
solution
Thus the pressure field within V is seen to be due to a distribution of point sources of
strength
located on the piston surface S. The total pressure field is simply obtained by superposition
of all the corresponding impulse responses, as stated in (26). The pressure gradient on S
is known from (25b) and the Green's function G, has been calculated [see equation (22)]
previously for an arbitrary source location Fo. After some calculations, one generates the
pressure field within the cavity:
23
with
2nmx ) cos(-) 2nny COS[-(% “P + -)] Lz 2
* cos( - LZ Lv Lz
and
1 i = O
2 i # O (29)
1 Em En Ep
Am, = -E ; =
As expected, the response blows up if the excitation frequency w coincides with one of
the resonant frequencies w,,,,~.
In the low frequency limit w + 0, the general formula (27) simplifies considerably:
+ O ( W 2 ) , w + 0. POE&& c2 (30) P w ( T 3 = - LzLvLz
this relation provides a simple scaling relation at excitation frequencies which are far from
resonance frequencies. It is worth noticing that, in the low frequency limit, the pressure is
uniform within the cavity, at leading order.
The pressure pw at the center of the piston is given by
7.2 Results Based on Acoustic Analysis and Some Experiments
Programs have been written to display graphically the response curve pw(O, 0, L z / 2 ) given
by (31) as a function of excitation circular frequency w. Typical results are shown in Figures
23 and 24. The first few resonances appear to intrude into the frequency range of interest,
as seen from Figure 23 where one detects the pervading influence w0,1,0 (or wl,O,o) and of
24
*
0
e
0
0
0
w ~ , ~ , ~ . Figure 24 shows the pressure response in the lower part of the spectrum below the
1st resonance frequency. The exact location of the resonances is likely to be sensitive to the
shape of the cavity. The order of magnitude of p , outside the resonance regions is likely to
be fairly insensitive to. the particular shape of the cavity.
As a check on the validity of the analysis we observed pressures in the stagnation chamber
using the cavity disturbance technique. The cavity is illustrated in Figure 2 of Ref. 11. The
predicted cavity pressures as a function of frequency are shown in Figure 25 along with
several measured pressures. The “cavity” was cylindrical in shape so that the predictions
are only expected to be approximate. The piston is a piezoelectric crystal forming one end
of the cavity (see Figure 2, Ref. 11). The data points are the measured amplitudes of the
pressure fluctuations in the cavity. Note that the predictions and measurements are in order
of magnitude agreement.
Predictions were made for the multi-stream generator and are shown in Figure 26. For
this case because the area of the moving orifice array (see Figure 9) is relatively smaller
than in the cavity disturbance mode experiments, the low frequency pressures are smaller
(see Eqn. 30). Also, due to the configuration of the orifice assembly, significant structural
vibrations were transmitted and observed, making it impossible to measure cavity pressures
with our piezoelectric pressure transducer in the multi-stream droplet generator. Relying
on the prediction it is apparent that in future designs, using the orifice disturbance mode
of operation, it would be useful to have individual stagnation cavities for each orifice array,
such that the moving array and its mount form the complete surface area of the bottom
of each cavity. Such an arrangement will result in maximum pressure being achieved in
each stagnation cavity. For the present design, simply walling off each moving array would
increase the pressures and change its frequencies, as shown in Figure 27.
8 LARGE SCALE GENERATOR DESIGN
As part of the contract a preliminary design of a nominal 5000 orifice generator segment
was required. The large scale generator designs are shown in Figures 29 through 33. The
design is similar to the laboratory generator fabricated for this contract. The orifice distur-
25
bance mode of perturbation was employed in the design because of the advantages described
in section 4.2. It is believed that any shortcomings found in the results due to the ampli-
tude limitations of this mode of motion can be overcome by decreasing the stagnation cavity
volume as described in the previous section.
The proposed nominal 5000 stream generator segment incorporates walls associated with
the bottom plate of the generator (see Figure 31). The walls not only serve to reduce the
volume of the stagnation cavities but act to increase significantly the moment of inertia
of the bottom plate, thus making the design more efficient from a structural perspective.
Additionally, divider walls can be added at periodic intervals as illustrated in Figure 31,
which changes the resonance characteristics and also increases the structural integrity of
the bottom plate. The resulting pressure predictions are shown in Figure 28. Note the
disappearance of the resonant peaks at the lowest frequency. More work needs to be done,
however, to determine accurately the amplitudes required for highly uniform drops as a
function of fluid viscosity.
A schematic of the nominal 5000-orifice droplet generator is illustrated in Figure 29. This
particular schematic shows a cut-away of the generator, exposing the fluid supply duct, filter
plate and array assembly. The generator is 0.616 m (24.25 inches) long, and contains 20
arrays. Figure 30 shows a further cut-away illustrating the generator’s configuration. Figure
31 shows a top view and a side view of the array holder. The assembly was designed such
that the angular deflection due to bending of.the orifice array when subjected to a load’of
150 psi is less than 5 prad. Figure 32 shows a side view of the assembled generator. Lastly,
Figure 33 illustrates the orifice array assembly. Each of the 20 arrays can contain in a single
row 260 orifices which are 100 pm in diameter, at 5 diameter spacings. The mass of the
generator illustrated in Figure 29 and 31 is about 1.2 gms per orifice (5200 orifices) using
aluminum for the Structural components. For carbon fiber composite structural components
the mass is around 0.9 gms per orifice.
26
c
9 SUMMARY OF RESULTS
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A multi-stream laboratory generator was designed and fabricated in a pre-prototype
configuration which would be potentially suitable for use with a Liquid Droplet Radiator.
The generator was tested using two orifice arrays; one drilled by NASA Lewis, and the
other fabricated by Du Pont Precision. Two fluids with viscosities of lxlO-' m2/s (10
cSt) and 4x10-' m2/s (40 cSt) were also used. Stream speeds were 10, 20, and 30 m/s.
Angular dispersions of the streams from the 100 orifice Du Pont array were measured and no
significant variation with stream velocity was found. The 4 ~ 1 0 - ~ m2/s (40 cSt) fluid appears,
at around fgprad, to have smaller angular dispersion than the l ~ l O - ~ m2/s (10 cSt) fluid.
However, the resolution obtained when photographing the 4x10-' m2/s (40 cSt) streams
was much greater than the resolution obtained when photographing the I x ~ O - ~ m2/s (10
cSt) streams and in retrospect there was a possibility of dissolved gases in the fluid during
the 10 cSt experiments. Velocity dispersions were also measured. It was discovered that in
the parameter range that was investigated, the amplitude of the disturbance applied to the
stagnation cavity is an important parameter in obtaining ultra-coherent streams of droplets.
It is also presumed that the more viscous fluid requires a higher power to the crystal (larger
crystal deflection) than does the lower viscosity fluid, although this presumption must be
verified in future investigations. The velocity dispersions for streams from several positions
along the 0.13 m orifice array were similar.
A conceptual design for a 5200 stream generator was completed, incorporating ways
to generate higher disturbance amplitudes than was possible in the laboratory generator.
Otherwise the design is similar to that of the laboratory generator.
e
27
APPENDIX I: NOMENCLATURE
c speed of sound
d droplet diameter .
do orifice a nozzle diameter
G,( r' I F,) Green's functions
k non-dimensional wavenumber for acoustical analysis
I C , non-dimensional wavenumber for a capillary streams (( X/?rdo)-')
C,,, dimensions of surface containing the orifice array
L droplet flight length or characteristic dimensions in acoustic analysis
Lz,y,z dimensions of stagnation cavity
n droplet number density
5 unit normal vector
N frequency ratio of amplitude modulated waveform
N,, total number of collisions one droplet experiences
N, number of rows of droplet streams
p perturbation pressure
P, Prandtl number
T', source position vector
t time
V stagnation cavity volume
28
P perturbation velocity
V d speed of droplets
w, thickness of droplet sheet at generator
29
,f3 amplitude growth factor
7 ratio of specific heats
A thickness of sheet in radiation mean free paths
r
9 dilatational viscosity
8, angular error of stream alignment
A center to center spacing of drops, also disturbance wavelength of carrier waveform
amplitude of orifice array displacement
A,-J intra-stream separation
Agl geometric spacing of nozzles
Ag2 separation between rows
A, wavelength of disturbance imposed as a capillary stream
A quantity in acoustic analysis
u kinematic viscosity
p perturbation density
po density of liquid in stagnation cavity
u surface tension
ut collision cross-section of droplet
$,,, ,% ,nz eigenfunction
w circular frequency
30
References
IA.T. Mattick and A. Hertzberg. “The Liquid Droplet Radiator - an Ultralightweight
Heat Rejection System for Effective Energy Conversion in Space”, Acta Astronautica 9,
~ ~ 1 6 5 - 1 7 2 , 1982
2K.A. White. “Liquid Droplet Radiator Status,” AIAA preprint 87-1537, June 1987
3M.T. Plateau. “The Theory of Sound,” edited by Lord Rayleigh, Vol 11, New York, p360,
1945
4F. Savart. “Memoire sur la Constitution des Veins Liquides Lanceee par des Orifices Cir-
culaires en Mince Paroi,” Annles de Chimie, 53, pp337-386, 1833
5Lord Rayleigh. “On the Instability of Liquid Jets,” Proc. R. SOC. Lond., A29, p71, 1878
6M.C. Yuen. “Non-linear Capillary Instability of a Liquid Jet,” J. Fluid Mech., 33, Part 1,
~ ~ 1 5 1 - 1 6 3 , 1968
7A.H. Nayfeh. “Nonlinear Stability of a Liquid Jet,” Phys. of Fluids, 13,4, pp841-847,1970
8D.B. Bogy. “Drop Formation in a Circular Liquid Jet,” Ann. Rev. Fluid Mech., 11,
~ ~ 2 0 7 - 2 2 8 , 1979
9K.C. Chaudhary and L.G. Redekopp. “The Non-linear Capillary Instability of a Liquid
Jet, Part I,” J. Fluid Mech., 96, Part 2, pp257-274, 1980
l0M. Orme and E.P. Munta. “New Technique for Producing Highly Uniform Droplet Streams
Over an Extended Range of Disturbance Wavenumbers,” Rev. Sci. Instrum. 58, 2, pp279-
284, 1987
llE.P. Muntz and M. Orme (Dixon). “Applications to Space for Free Flying Streams of
Liquid Drops,” J. of Spacecraft, 23, 4, pp411-419, 1986
12M. Orme (Dixon). “The Droplet Velocity Dispersion Device,” AIAA Student Journal,
Spring issue, pp14-23, 1985 and AIAA Preprint 85-0077
31
4
13B. Stanley. Du Pont Precision: private communication, March, 1988
14P. Huerre. “Effects of Friction and Heat Conduction on Sound Propagation in Ducts,” 4 Ph.D. Dissertation Department of Aeronautics & Astronautics, Stanford University, 1976
15G. Kirchhoff. “Ueber den Einfluss der Warmeleitung in einem Gase auf die Schdbewe-
gund,” Ann. Phys. Lpz., 134, pp172-193, 1868 4
l6P.M. Morse and K.U. Ingard. “Theoretical Acoustics,” McGraw Hill, New York, 1968
32
0
0
8
DROPLET SIGXATURE
Figare 1: Dtopld profle trace obtained by positioning the optical slit on the center of the
droplet stream.
33
4
h
i i I
I
I
[ i 1
r! I
I I
I I ! - 1 i.
I - i I
j i I I i
Figure 2: Droplet profile trace obtained by positioning the detector on the edge of the droplet
stream in order to determine the angalat dispersion of the stream.
4
34
*
0
0
z 0 H rn IY W
In 0
P I-
v 0 J W >
a H
n
1 .E-S
I .E-6
I 0 KO - . 3
0
FREQUENCY RRTIO (Nj
Figare 3: Response of the stream to an amplitude modulated disturbance. N is the k p c n c y
ratio. N=L corresponds to a conventional constant amplitude sinusoidal vavefonn.
35
.---- id7 velocity dispersion iof - - - IOe6 velocity dispersion
t- / t /-
t00pm lmm ICm
Droplet Diameter, d
Figure 4: Distance a boplet stream can travel without sigplficant merging with velocity
dispersion and nondimensional wavenumber as paramet-.
36
0
e
a
m
a
Figure 5: Schematic of assembly of s e v e r a l generator modules.
37
e
a e
0 e e
* 0
K
Figure 6: Behavior of a single stream when disturbed with the cavity disturbance mode
of perturbation. Droplet fluid is DC-200: 1 x lows m3/s (LO cSt), n o d e diameter is 125
38
e
C
> t- n U 0 -I w >
1 . E-6 0
e
I " . ( - I Z , ' z ' , ' ' . ,
-
- -
0 I . , . 1 . . , 1 I . ,
0.0001
z 0 n ffl tY W n U ffl c1 I. E-5
0 0
0 . 0
0
O K
0
Figure 7: Behavior of a single stream when disturbed with the orifice disturbance mode of
perturbation. Droplet fluid is DC-200: lxl0" m2/s (LO cSt) , n o d e diameter is 125 microns
39
OSC ILLAT1 NG 0 R I FICE ASS€MlLY
Figure 8: Schematic of cross-section of generator module illustrating meam of perturbation
chosen for present design.
40
e
a
0.2"
I
0 . i s "
j 0.05"
I -
Figure 9: Schematic of the details of oriiice array assanbly.
41
Figure 10: Schematic of the apparatus used to test the multi-stream droplet generator:
Droplet Dynamics Space Simulator. 1
*
0
e
e
0
e Figure 11: Detector used to obser~e the droplet a;zeams.
43
I I I I I . '
-
T I I
I I
Figrue 12: Schematic of optical path and data retrieval methods.
4
I
1
Figure 13: Photograph dustrating the generator performance with the 100 hole a.rray which
w a manllfactared by Du Pont Predsion.
ORlGlN.9L PAGE BLACK AND WHITE PHOTOGRAPH
45
Figuxe 14: Droplet stream waveform (lower trace) and perturbation waveform (upper trace)
obtained kom the 100 hole Du Pont h a y . I
48
< 5 .so
I 4.78 rn 0
e
a
a
0 Figure 15: Schematic of four hole NASA Lewis array.
14
47
o.coo1
Z 0 w
w e z I . E-5 C
L .E" (
0 1 1 . 2 W S A 2 ! 0 3 0
0 0
0 & A 0 0
0 0 0
1 j
i I i 1
i i i
I 1
I I
I I -
, . . . . . . . I . . . . . . . I . . . . . . , ' .
3 0.4 0 .5 0.5 0.7
Figure 16: Veiodty dispersions as a function of non-dimensional wavenumber for streams
generated horn orifice +l of the NASA Lewis axray with 1x10'' m2/s (10 cSt) DC-200.
!a Cf =u12, CRfFfCE S t 0.0301, I ' 1 " '
L .E+
0 1 ! . 2 M / S 4 2 1 n/s
I . . . . . . . . . ~ . . . . . . . . . ' . . ' . ' " ' L
0 30
0 O A 0
B 0
0
0
u 1 0 l
i i w >
I
1 - 1
I
1 i i I
1 i I
i
I
Figure 17: Veloaty dispersions as a function of non-dimensional wavennmber for streams
generated &om orifice #2 of the NASA Lewis arzay with 1x10'' m'/s (10 cSt) DC-200.
49
10 CS FLUIg, ORIFICE +3 0 . 0 0 O t ~ ' ' . ' ' ' ' ' L ' ' ' ' ' ' ' ' 1 " " - ' ' ' ' " ' . ' ' ' ' ' i
t I
I i
0 = I - i c1
! U 0 J u >
t I
0 2 0 . 0 n/S 0 3 0 . a W S Q 1 1 . 2 n/S
0 0
0
0 0
A 0
0
(1
0
1
! . E-5 I . . . . . . . . , I
0.3 0.4 0.5 0.5 0 . 7
Figure 18: Velocity disperzio~u as a function of non-dimensional wavenumber for streams
generated fiom o d c e +3 of the NASA Lewis array with l x l O - ' mz/s (10 cSt) DC-200.
50
! . E-5
a
i I . . . ) .
a
z 0
UY m
e
iz w t cn n s
U 0
w >
c A
h
c
C
Figare 19: Vdocity dispersions a a function of aon-dimensional wavenumber for streams
generated from orifice #l of the NASA Lewis array with 4X1O" m2/s (40 &t) DC-200.
51
I a
0
a
Figure 20: Vdocity dispersions as a function of non-dimauiond wavenumber for streams
generated &om orifice #2 of the NASA Lewis auay with 4x10'' mZ/s (40 cSt) DC-200.
52
z 0
l c-3 ..a
cn C
E
I
G C 20.0 R/S
I I i
c U 0
Figure 21: Velocity dispersions as a function of non-dimensional wavenumber for streams
guerated from o d c e #3 of the NASA Lewis array with WO" m2/s (40 cSt) DC-200.
53
i‘
Figure 22: General codiguratioa for acoustic analysis.
,
0 Figure 23: Remits of acoustic analysis.
,
55
0 . sox I o3 3 looxlo CYCLIC FREQUENCY
Figure 24: Besults of acoustic analysis.
56
i I 4
i i !
L I
I -. !7
I i r r L
i
t ! i
1
Figure 25: Prediction of cavity pressure as a bction of frequency for the cayity disturbance
mode of operation. Experimental points are absolute values since no documentation of phase
was made.
57
Figuse 26: Prediction of cavity pressure as a function of ikcquency for the mdti-stream
generator with a single large cavity.
0
I
Figure 27: Prediction of cavity pressure as a function of frequency for the generator c o d g -
uration of five sepaate cavitia; one for each array.
59
Figure 28: Prediction of cavity pressure a a function of &equency for the generator config-
uration of 20 separate cavities, four cavities to one array.
60
Figure 29: Schematic of nominal 5000-orifice droplet generator.
61
Figure 30: Schematic of generator illustrating configuration.
62
Figare 31: Schematic of top view and bottom view of array holder.
63
Figure 32: End cross-section view of assembled generator.
64
a
I a
Figure 33: Schematic of orifice anay assembly.
65
1. R e m No. NASA CR-182246
N a t i o n a l Aeronaut ics and Space A d m i n i s t r a t i o n Lewis Research Center C 1 eve land, Oh i o 44 135-3 191
2 Gowmment Accession NO. 3. Recipient's Camkg NO.
I
5. Supplmnenwy Nota
P r o j e c t Manager, K. A lan White, Power Technology D i v i s i o n , NASA Lewis Research Center (216) 433-6165
4. Tdle and SubtiUe
Design and Performance o f a D r o p l e t Generator Module f o r t he L i q u i d D r o p l e t Rad ia to r
7. -4
E . P . Muntz, Me l i ssa Orme, Tony Farnham
16. Abnnn
A p r e - p r o t o t y p e segment o f a d r o p l e t sheet genera to r f o r a l i q u i d d r o p l e t r a d i a t o r has been designed, c o n s t r u c t e d and t e s t e d . The a b i l i t y t o ach ieve a un i fo rm, non- d i v e r g i n g d r o p l e t sheet i s l i m i t e d by manu fac tu r ing to le rances on n o z z l e p a r a l l e l - ism. For an a r r a y o f 100, 100pmd ia . nozz les spaced 5 stream diameters a p a r t , t y p i c a l s tandard d e v i a t i o n s i n stream al ignment were 2 10 mrad. The d rop to. drop f r a c t i o n a l speed v a r i a t i o n s o f t h e drops i n t y p i c a l streams were s i m i l a r and independent o f p o s i t i o n i n t h e a r r a y . The a b s o l u t e v a l u e o f t h e speed d i s p e r s i o n depended on t h e amp l i t ude o f t h e d i s t u r b a n c e a p p l i e d t o t h e stream. g e n e r a t i o n p r e l i m i n a r y des ign o f a.5200 stream segment o f a d r o p l e t sheet generator has been completed. The des ign i s based on i n f o r m a t i o n developed d u r i n g t e s t i n g of the p r e - p r o t o t y p e segment, a l o n g w i t h t h e r e s u l t s o f an a c o u s t i c a l a n a l y s i s f o r the s t a g n a t i o n c a v i t y p ressu re f l u c t u a t i o n s used t o break-up t h e streams i n t o d r o p l e t s .
A second
5. Repon Date
June 1989 6. Pedorming Organization Code
8. Performing Org8niiutiOn Repon No.
10. won Unil No. 506-41 -51
0. Putomring OrOuJnlion Name and Address
U n i v e r s i t y o f Southern Cal i f o r n i a Department o f Aerospace Eng i neer i ng Los Angeles, C a l i f o r n i a 90089-1191
2 sponrorhg Agency Name and Addran
11. Coninel of G m t No.
NAS3-2 5068
13. Typo d Report and Period -red
Cont rac to r Report F i n a l
17. K y W?r6 (Suggested by mi)) Drop1 e t Genera t o r L i q u i d D r o p l e t Rad ia to r Cav i t y Acous t i cs
18. O & t b l h Statement
U n c l a s s i f i e d - U n l i m i t e d Sub j ec t Ca tego r i es 20,34
19. 3mnity classif. (d thb mpoq 20. 3rcuity Quril. (of thh -0.) U n c l a s s i f i e d U n c l a s s i f i e d
21. No e4 p 0 . s ZL P*' 65 A0 4
